An efficient preconditioned iterative solution of fully-coupled elastohydrodynamic lubrication problems

This paper presents the fast preconditioned iterative solution to large sparse linear systems arising from the application of Newton and quasi-Newton methods to fully coupled elastohydrodynamic lubrication line and point contact problems. The new blockwise preconditioner that is presented combines the use of multigrid for the linear elasticity block and a separate approximation to precondition the Reynolds block. Two variants of the solver are considered, based upon the use of algebraic and geometric multigrid respectively. Numerical results are presented in order to validate the discretization and solution method and then to contrast the performance and efficiency of the proposed solution strategies compared to the use of a state-of-the-art sparse direct solver. These results demonstrate that, unlike the sparse direct solver, the preconditioned iterative approach is able to perform at computational and memory costs that both grow linearly with the number of unknowns.